Graph algebras

by
Prof.Roozbeh HAZRAT
(University of Western Sydney & IHES)

Tuesday
21 Jan 2014, 15:30
→
16:00
Europe/Paris

Amphitéâtre Léon Motchane (IHES)

Amphitéâtre Léon Motchane

IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

From a graph (e.g., cities and flights between them) one can generate an algebra which captures the movements along the graph. This talk is about one type of such correspondences, i.e., Leavitt path algebras. Despite being introduced only 8 years ago, Leavitt path algebras have arisen in a variety of different contexts as diverse as analysis, symbolic dynamics, noncommutative geometry and representation theory. In fact, Leavitt path algebras are algebraic counterpart to graph C*-algebras, which has become an area of intensive research. There are strikingly parallel similarities between these two theories. Even more surprisingly, one cannot (yet) obtain the results in one theory as a consequence of the other; the statements look the same, however the techniques to prove them are quite different (as the names suggest, one uses Algebra and other Analysis). These all suggest that there might be a bridge between Algebra and Analysis yet to be uncovered. In this talk, we introduce Leavitt path algebras and then try to understand the behaviour and to classify them by means of (graded) K-theory. We will ask nice questions!